Integrand size = 20, antiderivative size = 44 \[ \int \frac {(1-2 x) (2+3 x)^4}{3+5 x} \, dx=\frac {16663 x}{3125}+\frac {7779 x^2}{1250}-\frac {531 x^3}{125}-\frac {1269 x^4}{100}-\frac {162 x^5}{25}+\frac {11 \log (3+5 x)}{15625} \]
[Out]
Time = 0.01 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {78} \[ \int \frac {(1-2 x) (2+3 x)^4}{3+5 x} \, dx=-\frac {162 x^5}{25}-\frac {1269 x^4}{100}-\frac {531 x^3}{125}+\frac {7779 x^2}{1250}+\frac {16663 x}{3125}+\frac {11 \log (5 x+3)}{15625} \]
[In]
[Out]
Rule 78
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {16663}{3125}+\frac {7779 x}{625}-\frac {1593 x^2}{125}-\frac {1269 x^3}{25}-\frac {162 x^4}{5}+\frac {11}{3125 (3+5 x)}\right ) \, dx \\ & = \frac {16663 x}{3125}+\frac {7779 x^2}{1250}-\frac {531 x^3}{125}-\frac {1269 x^4}{100}-\frac {162 x^5}{25}+\frac {11 \log (3+5 x)}{15625} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 37, normalized size of antiderivative = 0.84 \[ \int \frac {(1-2 x) (2+3 x)^4}{3+5 x} \, dx=\frac {369411+1666300 x+1944750 x^2-1327500 x^3-3965625 x^4-2025000 x^5+220 \log (3+5 x)}{312500} \]
[In]
[Out]
Time = 2.20 (sec) , antiderivative size = 31, normalized size of antiderivative = 0.70
method | result | size |
parallelrisch | \(-\frac {162 x^{5}}{25}-\frac {1269 x^{4}}{100}-\frac {531 x^{3}}{125}+\frac {7779 x^{2}}{1250}+\frac {16663 x}{3125}+\frac {11 \ln \left (x +\frac {3}{5}\right )}{15625}\) | \(31\) |
default | \(\frac {16663 x}{3125}+\frac {7779 x^{2}}{1250}-\frac {531 x^{3}}{125}-\frac {1269 x^{4}}{100}-\frac {162 x^{5}}{25}+\frac {11 \ln \left (3+5 x \right )}{15625}\) | \(33\) |
norman | \(\frac {16663 x}{3125}+\frac {7779 x^{2}}{1250}-\frac {531 x^{3}}{125}-\frac {1269 x^{4}}{100}-\frac {162 x^{5}}{25}+\frac {11 \ln \left (3+5 x \right )}{15625}\) | \(33\) |
risch | \(\frac {16663 x}{3125}+\frac {7779 x^{2}}{1250}-\frac {531 x^{3}}{125}-\frac {1269 x^{4}}{100}-\frac {162 x^{5}}{25}+\frac {11 \ln \left (3+5 x \right )}{15625}\) | \(33\) |
meijerg | \(\frac {11 \ln \left (1+\frac {5 x}{3}\right )}{15625}+\frac {64 x}{5}-\frac {12 x \left (-5 x +6\right )}{25}-\frac {162 x \left (\frac {100}{9} x^{2}-10 x +12\right )}{125}+\frac {3159 x \left (-\frac {625}{9} x^{3}+\frac {500}{9} x^{2}-50 x +60\right )}{12500}-\frac {2187 x \left (\frac {2500}{27} x^{4}-\frac {625}{9} x^{3}+\frac {500}{9} x^{2}-50 x +60\right )}{31250}\) | \(75\) |
[In]
[Out]
none
Time = 0.21 (sec) , antiderivative size = 32, normalized size of antiderivative = 0.73 \[ \int \frac {(1-2 x) (2+3 x)^4}{3+5 x} \, dx=-\frac {162}{25} \, x^{5} - \frac {1269}{100} \, x^{4} - \frac {531}{125} \, x^{3} + \frac {7779}{1250} \, x^{2} + \frac {16663}{3125} \, x + \frac {11}{15625} \, \log \left (5 \, x + 3\right ) \]
[In]
[Out]
Time = 0.04 (sec) , antiderivative size = 41, normalized size of antiderivative = 0.93 \[ \int \frac {(1-2 x) (2+3 x)^4}{3+5 x} \, dx=- \frac {162 x^{5}}{25} - \frac {1269 x^{4}}{100} - \frac {531 x^{3}}{125} + \frac {7779 x^{2}}{1250} + \frac {16663 x}{3125} + \frac {11 \log {\left (5 x + 3 \right )}}{15625} \]
[In]
[Out]
none
Time = 0.19 (sec) , antiderivative size = 32, normalized size of antiderivative = 0.73 \[ \int \frac {(1-2 x) (2+3 x)^4}{3+5 x} \, dx=-\frac {162}{25} \, x^{5} - \frac {1269}{100} \, x^{4} - \frac {531}{125} \, x^{3} + \frac {7779}{1250} \, x^{2} + \frac {16663}{3125} \, x + \frac {11}{15625} \, \log \left (5 \, x + 3\right ) \]
[In]
[Out]
none
Time = 0.29 (sec) , antiderivative size = 33, normalized size of antiderivative = 0.75 \[ \int \frac {(1-2 x) (2+3 x)^4}{3+5 x} \, dx=-\frac {162}{25} \, x^{5} - \frac {1269}{100} \, x^{4} - \frac {531}{125} \, x^{3} + \frac {7779}{1250} \, x^{2} + \frac {16663}{3125} \, x + \frac {11}{15625} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \]
[In]
[Out]
Time = 0.03 (sec) , antiderivative size = 30, normalized size of antiderivative = 0.68 \[ \int \frac {(1-2 x) (2+3 x)^4}{3+5 x} \, dx=\frac {16663\,x}{3125}+\frac {11\,\ln \left (x+\frac {3}{5}\right )}{15625}+\frac {7779\,x^2}{1250}-\frac {531\,x^3}{125}-\frac {1269\,x^4}{100}-\frac {162\,x^5}{25} \]
[In]
[Out]